On the solution to the Riemann problem for the compressible duct flow

SIAM Journal on Applied Mathematics

Volumn 64, Issue 3, 2004, Pages 878-901

  Andrianov, Nikolai ^a   Warnecke, Gerald ^a  

^a OTTO VON GUERICKE UNIVERSITY   (Germany)

Author keywords

Nonstrictly hyperbolic; Nozzle flow; Resonance

Indexed keywords

DUCTS; ENTROPY; MATHEMATICAL MODELS; NONLINEAR EQUATIONS; NOZZLES; PROBLEM SOLVING; RESONANCE;

EULER EQUATIONS; NONSTRICTLY HYPERBOLIC; NOZZLE FLOWS; RIEMANN PROBLEMS;

COMPRESSIBLE FLOW;

EID: 3142733781     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139903424230     Document Type: Article

References (18)

1. R. ABGRALL AND R. SAUREL, Discrete equations for physical and numerical compressible multiphase mixtures, J. Comput. Phys., 186 (2003), pp. 361-396.
2. N. ANDRIANOV, Analytical and numerical investigation of two-phase flows, Ph.D. thesis, Institut für Analysis und Numerik, Universität Magdeburg, 2003; available athttp://www-ian.math.uni-magdeburg.de/home/andriano/ diser.html.
3. N. ANDRIANOV, CONSTRUCT: A collection of MATLAB routines for constructing the exact solution to the Riemann problem for the Baer-Nunziato model of two-phase flows, available at http://www-ian.math.uni-magdeburg.de/home/ andriano/CONSTRUCT.
4. N. ANDRIANOV AND G. WARNECKE, The Riemann problem for the Baer-Nunziato model of two-phase flows, J. Comput. Phys., 195 (2004), pp. 434-464.
5. M. R. BAER AND J. W. NUNZIATO, A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials, Int. J. Multiphase Flows, 12 (1986), pp. 861-889.
6. CLAWPACK software, available at http://www.amath.washington.edu/~claw.
7. R. COURANT AND K. O. FRIEDRICHS, Supersonic Flow and Shock Waves, Springer, New York, 1999.
8. C. DAPERMOS, The entropy rate admissibility criterion for solutions of hyperbolic conservation laws, J. Differential Equations, 14 (1973), pp. 202-212.
9. C. DAFERMOS, Hyperbolic Conservation Laws in Continuum Physics, Springer, Berlin, 2000.
10. G. DAL MASO, P. G. LEFLOCH, AND F. MURAT, Definition and weak stability of nonconservative products, J. Math. Pures Appl., 74 (1995), pp. 483-548.
11. S. A. E. G. FALLE AND S. S. KOMISSAROV, On the inadmissibility of non-evolutionary shocks, J. Plasma Phys., 65 (2001), pp. 29-58.
12. P. GOATIN AND P. G. LEFLOCH, The Riemann problem for a class of resonant hyperbolic systems of balance laws, preprint, Ecole Polytechnique, Palaiseau, France, 2003; available at http://www.math.ntnu.no/conservation/2003/008.html.
13. E. GODLEWSKI AND P.-A. RAVIART, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer, New York, 1996.
14. E. ISAACSON AND B. TEMPLE, Nonlinear resonance in systems of conservation laws, SIAM J. Appl. Math., 52 (1992), pp. 1260-1278.
15. E. ISAACSON AND B. TEMPLE, Convergence of the 2 × 2 Godunov method for a general resonant nonlinear balance law, SIAM J. Appl. Math., 55 (1995), pp. 625-640.
16. L. D. LANDAU AND E. M. LIPSCHITZ, Fluid Mechanics, Pergamon Press, Oxford, 1987.
17. R. J. LEVEQUE, Wave propagation algorithms for multi-dimensional hyperbolic systems, J. Comput. Phys., 131 (1997), pp. 327-353.
18. M. J. ZUCROW AND J. D. HUFFMAN, Gas Dynamics, Vol. 2, John Wiley & Sons, New York, 1977.